Constructive dimension equals Kolmogorov complexity

Authors:
Ludwig Staiger
Affiliations:
Martin-Luther-Universität Halle-Wittenberg, Institut für Informatik, Seckendorff-Platz 1, D-06099 Halle, Germany
Venue:
Information Processing Letters
Year:
2005

Citing 9
Cited 5

Kolmogorov complexity and Hausdorff dimension

Information and Computation
The complexity and effectiveness of prediction algorithms

Journal of Complexity
Regular Article: On hausdorff and topological dimensions of the kolmogorov complexity of the real line

Proceedings of the 30th IEEE symposium on Foundations of computer science
An introduction to Kolmogorov complexity and its applications (2nd ed.)

An introduction to Kolmogorov complexity and its applications (2nd ed.)
A Kolmogorov complexity characterization of constructive Hausdorff dimension

Information Processing Letters
The Kolmogorov complexity of real numbers

Theoretical Computer Science
Gales suffice for constructive dimension

Information Processing Letters
Dimension in Complexity Classes

SIAM Journal on Computing
The dimensions of individual strings and sequences

Information and Computation

Algorithmically Independent Sequences

DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Algorithmically independent sequences

Information and Computation
Two sources are better than one for increasing the Kolmogorov complexity of infinite sequences

CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Constructive dimension and Hausdorff dimension: the case of exact dimension

FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Schnorr dimension

CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms

Quantified Score

Hi-index	0.89

Visualization

Abstract

We derive the coincidence of Lutz's constructive dimension and Kolmogorov complexity for sets of infinite strings from Levin's early result on the existence of an optimal left computable cylindrical semi-measure M via simple calculations.